The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 16
Wherefore from the given point A a straight line AL . has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the less .
Wherefore from the given point A a straight line AL . has been drawn equal to the given straight line BC . Which was to be done . PROP . III . PROB . FROM the greater of two given straight lines to cut off a part equal to the less .
Σελίδα 19
1 . equal to AC , the less , and join DC ; thereA fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to D both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal ...
1 . equal to AC , the less , and join DC ; thereA fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to D both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal ...
Σελίδα 26
ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any A two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ...
ANY two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any A two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ...
Σελίδα 27
In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the ...
In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle is opposite to the ...
Σελίδα 28
Book I. but it is not ; therefore the side AC is not less than AB ; and it has been shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . See Note .
Book I. but it is not ; therefore the side AC is not less than AB ; and it has been shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . See Note .
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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD added altitude angle ABC angle BAC arch base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 17 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Σελίδα 35 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 67 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Σελίδα 92 - IF a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 26 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.
Σελίδα 55 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made of the whole and that part.
Σελίδα 318 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 22 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 161 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα 21 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |
| Συγγραφέας | Euclid |
| Εκδότης | Conrad and Company, 1810 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 21 Ιουν. 2006 |
| Μέγεθος | 518 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |